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Potentialities of flexoelectric effect in soft polymer filmsfor electromechanical applications

Benoit Guiffard, Maria Saadeh, Pierre Frère, Raynald Seveno, MohammedEl-Gibari, Tessnim Sghaier, Victor Merupo, Adi Kassiba

To cite this version:Benoit Guiffard, Maria Saadeh, Pierre Frère, Raynald Seveno, Mohammed El-Gibari, et al.. Potential-ities of flexoelectric effect in soft polymer films for electromechanical applications. Journal of Physics:Conference Series, IOP Publishing, 2019, Electrostatics 2019 and Dielectrics 2019 8–12 April 2019,Manchester, UK, 1322, pp.012041. �10.1088/1742-6596/1322/1/012041�. �hal-02318718�

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Potentialities of flexoelectric effect in soft polymer films forelectromechanical applicationsTo cite this article: Benoit Guiffard et al 2019 J. Phys.: Conf. Ser. 1322 012041

 

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Electrostatics 2019 and Dielectrics 2019

IOP Conf. Series: Journal of Physics: Conf. Series 1322 (2019) 012041

IOP Publishing

doi:10.1088/1742-6596/1322/1/012041

1

Potentialities of flexoelectric effect in soft polymer films for

electromechanical applications

Benoit Guiffard1, Maria Saadeh1,2, Pierre Frère2, Raynald Seveno1, Mohammed

El-Gibari1, Tessnim Sghaier1, V I Merupo1,3 and Adi Kassiba3

1 Université de Nantes, IETR UMR CNRS 6164, France 2 Université d’Angers, MOLTECH-Anjou UMR CNRS 6200, France 3 Université du Maine, IMMM-UMR CNRS 6283, France

Benoit.guiffard@univ-nantes.fr

Abstract. Among the transduction mechanisms of interest for sensing and/or actuation

applications at nano/micro scale, the piezoelectric effect has been widely exploited owing to

the solid state nature of piezoelectrics, the large ability of specific classes of materials for the

mechanical-to-electrical energy conversion and easy integration. However, every piezoelectric

(also generally ferroelectric) presents well-known intrinsic drawbacks such as required poling

step and related aging. In contrast, uniquely flexoelectric materials do not suffer from these

disadvantages because flexoelectricity, a universal effect in all dielectric solids defined as the

electrical polarization induced by a strain gradient, does not imply preliminary electric field-

induced macroscopic polarization. Besides, strain gradient may be easily obtained by bending

plate or cantilever-shaped structure and in this case it is nothing but the local curvature of the

flexible system. Thus, as strain gradient (curvature) inversely scales with both elastic stiffness

and thickness, this study will focus on the evaluation of the potentialities of flexoelectric effect

in soft polymer films for electromechanical applications, with an emphasis on the thickness

influence. In this way, analytical results combined to experimentally obtained effective

flexoelectric coefficients for some typical polymer classes may provide guidelines for the

development of soft and low frequency flexoelectric mechanical transducers.

1. Introduction

Although it was theoretically described in the late eighties by Tagantsev [1], flexoelectricity, which is

a linear electromechanical coupling, has recently become a hot topic in the materials science

community, in the last 5 years. The main reason of this revival is the possibility to exploit flexoelectric

effect in micro/nano electromechanical systems (MEMS/NEMS), being currently developed for both

sensing and actuation applications along with the ongoing advances in nanotechnology. As a matter of

fact, direct flexoelectricity, which is a universal effect in all solid dielectrics corresponds to the

appearance of an electric polarization induced by a strain gradient, defined for instance in the

thickness direction by 𝑃3𝑓𝑙𝑒𝑥 = 𝜇1133𝜕𝑆11

𝜕𝑥3 (1), where 𝜇1133 is the transverse flexoelectric coefficient,

𝑆11 is the axial strain (1-direction is the axial direction of the clamped cantilever-shaped sample in

figure 1) and 𝑥3 is the position coordinate along thickness direction. Thus, although flexoelectric

coefficients are presently two or three orders of magnitude lower than piezoelectric ones (𝑒31),

yielding the electrical polarization 𝑃3𝑝𝑖𝑒𝑧𝑜 = 𝑒31𝑆11 (2), strain gradients may reach huge values at

small scales, up to 106 m-1 , for instance in epitaxial thin films. Clearly, the strain gradients in thin

films are significantly larger than the corresponding strain values (1%) and the strain gradients in the

bulk form of the material, so 𝑃3𝑓𝑙𝑒𝑥 may exceed 𝑃3𝑝𝑖𝑒𝑧𝑜in specific cases. Bibliography on

Electrostatics 2019 and Dielectrics 2019

IOP Conf. Series: Journal of Physics: Conf. Series 1322 (2019) 012041

IOP Publishing

doi:10.1088/1742-6596/1322/1/012041

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flexoelectricity in elastic dielectrics reveals that in the last ten years many studies have been devoted

to both theoretical and experimental works on oxides (bulk and thin film forms), and two major trends

have been demonstrated and validated. First, flexoelectric coefficients scale with the dielectric

constant (K). So, high-K materials should be privileged for obtaining the best flexoelectrics. For

instance, perovskite materials like Barium Strontium Titanate (BST) ceramic [2] exhibits the largest

flexoelectric coefficients, in the range 10-6-10-5 C/m, associated with a large K (13000). Second, the

flexocoupling coefficient 𝐹, defined as the ratio of µ coefficient over the dielectric constant K: 𝐹 = µ/𝜀0𝐾 (3), where 𝜀0 is the vacuum permittivity, should be quasi constant and lie between 1 V and 10

V, independently on the thickness [3]. Compared with oxide films, few studies have been devoted to

the flexoelectric effect in organic materials but it was recently published that flexoelectric coefficients

in thermoplastic and thermosetting polymer thick (500 µm) films of PVDF (polyvinylidene fluoride

in its non-piezoelectric form) or polyethylene (PE) are about 1-10 nC/m [4]. Even if these µ

coefficients are three orders lower than those of BST bulk ceramics, the flexibility (i.e. low Young’s

modulus Y) and lightweight of soft polymers render them interesting for sensing and actuating

applications. Thus, in the present study, we report experimental results on the thickness dependence of

the effective transverse flexoelectric and flexocoupling coefficients of some soft polymer films and

analytical results to assess if their use may be envisaged as transducer materials in specific

applications such as mechanical energy harvesting or curvature sensing.

Figure 1. Experimental set-up for

flexoelectric characterisation with

a cantilever-shaped bilayer

(flexoelectric/passive steel

substrate) deflected by base

oscillations

2. Experimental procedure

The studied polymers have been selected for their relative softness (Y<1GPa) and for their different

global polarity: a polyurethane (PU) grade, which is a semi-crystalline thermoplastic elastomer with a

block copolymer morphology. Non-piezoelectric but polar (α-form) PVDF and also a semi-conducting

polythiophene (PT)-based blend have also been tested. The two former polymers are considered to be

insulating while the latter (PT blend) exhibits a semi-conducting behavior. The 200 µm-thick PU

polymer films have been prepared by dissolving the commercially available granules in N, N-

dimethylformamide (DMF) and the solutions have been homogeneously poured onto a stainless steel

substrate using a film applicator and then dried at 40C for 20 h and subsequently annealed at 130C

for 3 h. PU and PVDF films with thicknesses lower than 5 µm have been prepared by spin coating

onto the same substrate. Then, the deposited films were annealed on a hot plate at 95C for 5 min to

evaporate excess of DMF. PT-blend films have been deposited onto stainless steel substrate by drop

casting method using a commercial aqueous PT solution and dried at 60°C for 2h. The resulting

thicknesses lie between 3 and 8 µm. The stiff (200 µm thick and Y=209 GPa) stainless steel substrate

serves both as a bottom electrode and also as a supporting layer to ensure a pure bending mode of the

cantilevered beam (figure 1) clamped at one end. In fact, the beam deflection magnitude must be

smaller than the dimensions of the cantilever to use the assumptions of the Euler-Bernoulli beam

theory. In this case, the local beam curvature used for the determination of the flexoelectric coefficient

may be calculated from the measured deflection. Experimental and calculation details are given in our

previous work [5]. A top point electrode of Aluminum with 100 nm in thickness was deposited by

evaporation on the top surface of the polymer/steel bilayer (unimorph structure) for dielectric and

direct flexoelectric measurements. Direct (current output) flexoelectric effect have been measured

using a lock-in amplifier tuned to the frequency of the applied curvature (i.e. controlled cantilever

bending).

Flexoelectric

(soft polymer) clamp

Cantilever beam

(stiff supporting layer)

1

3

Base

oscillations

2

Beam

deflection

Electrostatics 2019 and Dielectrics 2019

IOP Conf. Series: Journal of Physics: Conf. Series 1322 (2019) 012041

IOP Publishing

doi:10.1088/1742-6596/1322/1/012041

3

3. Results and discussion

3.1. Flexoelectric and flexocoupling coefficients

Figure 2 shows the direct effective flexoelectric coefficients measured at 10 Hz as a function of the

thickness, in quasistatic condition since the first resonance frequency of the unimorph cantilevers is

close to 165 Hz, imposed by the stiff supporting steel layer.

Figure 2. Flexoelectric coefficient µ of the

polymer films versus thickness.

Figure 3. Flexocoupling constant F of the

polymer films versus thickness.

The PU and PVDF films exhibit µ coefficients in the 1 nC/m- 30 nC/m range, with a slight thickness

dependence. These results are consistent with the µ coefficients previously given in the literature for

such insulating polymer films [4]. In comparison, the semi-conducting PT blend films present very

large flexoelectric-like µ coefficients, because, by definition, only dielectrics are flexoelectric. The

largest µ of the PT blend series is 7300 nC/m, with a decrease with increasing thickness, even if

further film thicknesses should be tested to confirm the trend. The thickness dependence of the

flexocoupling constant F is more obvious (figure 3), but the largest F values are globally obtained for

PVDF and PU films, in the 1-10 µm range. This opposite trend in comparison with that of µ

coefficient is due to the huge dielectric constants measured at 100 Hz of the PT series (K6000-

19000), significantly larger than those of PVDF and PU series (7-10). Finally, figures 2 and 3 reveal

that very large flexoelectric-like coefficients may be achieved, in agreement with a scaling effect with

the dielectric constant, but the F coefficient, which is of significant importance because it reflects the

curvature ()-induced flexoelectric field E (E=F. ), is not necessarily enhanced by large µ values.

Besides, the order of magnitude F coefficient of the studied polymers may reach large values [6], in

comparison with the theoretical estimate (1-10 V)[3], experimentally validated in many oxides. These

results strongly suggest that the measured response is not only due to bulk effect but also surface

contributions like the so-called surface flexoelectricity and possibly surface piezoelectricity [3],

depending on the insulating or moderately conducting nature of the polymer.

3.2. Flexoelectric energy conversion

Figure 1 represents the typical case of base-excited cantilever, which is a widely used structure in the

field vibration energy harvesting using piezoelectric material clamped on the stiff beam. In the case of

flexoelectric energy conversion, the same unimorph structure may be employed but also more simply

a single flexoelectric cantilever without supporting layer since strain gradients (i.e. cantilever

curvature) are the consequence of beam bending, whatever the location of the neutral axis. For

estimating the potential of the studied polymer films, a Figure of Merit (FoM) for energy harvesting is

proposed from a simple electrokinetic model, where the flexoelectric film is modelled by a current

source in parallel with its clamped capacitance [7] and connected to a resistive electrical load, in

which the dissipated power density equals the harvested one. For a fixed flexocoupling coefficient F,

the optimal harvested power density as a function of the curvature is expressed by: 𝑃 =

Electrostatics 2019 and Dielectrics 2019

IOP Conf. Series: Journal of Physics: Conf. Series 1322 (2019) 012041

IOP Publishing

doi:10.1088/1742-6596/1322/1/012041

4

µ2𝜔/(𝜀0𝐾) (4), where 𝜔 is the angular frequency of the beam vibrations. Thus, from the viewpoint

of the material, the Figure of Merit is 𝐹𝑜𝑀 = µ2/(𝑌𝐾)(5), since under a fixed base excitation, increases with decreasing Y.

Figure 4. Figure of Merit for flexoelectric

energy conversion of the polymer films

versus thickness.

Figure 4 gives the FoM of the different polymer films as function of the thickness. The FoM was

calculated using the bulk Young’s modulus of the polymer, obtained from literature or supplier data.

Figure clearly shows that thin (<10 µm) films of PU and PT blend present the best characteristics

combination for flexoelectric energy harvesting purpose. The difference between the FoM of PU and

PVDF mainly originates from their difference in Young’s modulus (YPU=28 MPa and YPVDF=1.1

GPa), because their µ and K coefficients are of the same order of magnitude. Despite their huge

dielectric constant values, the large flexoelectric µ coefficient of PT blend films (figure 1) contributes

to the large FoM since the elastic modulus YPT blend=700 MPa is close to that of PVDF.

4. Conclusion

In this study, quasistatic flexoelectric current measurements have been carried out for three polymer

film series in the 1-100 µm range: polyurethane (PU), polyvinylidene fluoride (PVDF) and

polytiophene based compound (PT blend). The semi-conducting PT blend films present the largest

flexoelectric-like µ coefficients (up to 7000 nC/m), in comparison with the µ coefficients of PU and

PVDF in the 10 nC/m range. Two figures of merit have been calculated from measured flexoelectric

and dielectric characteristics: the fundamental flexocoupling F coefficient, which is high for PU and

PVDF films and the FoM for flexoelectric energy conversion (harvesting), which highlights the

potential of both PU and PT blend. These measurements and given trends indicate that the

flexoelectric µ coefficient is not the only key factor determining the ability for a polymeric material to

be integrated in electromechanical applications. Thus, high µ value may be suitable for curvature

sensing, but not necessarily for mechanical energy harvesting. At last, the thickness dependence of the

coefficients accompanied with large F values may originate from surface contributions, which need to

be experimentally evaluated.

5. References

[1] Tagantsev AK 1986 Phys Rev B 34(8) 5883

[2] Ma W, Cross LE 2002 Appl Phys Lett 81(18) 3440.

[3] Zubko P, Catalan G, Tagantsev AK 2013 Annu Rev Mater Res. 43(1) 387

[4] Chu B, Salem DR 2012 Appl Phys Lett. 101(10) 103905.

[5] Merupo VI, Guiffard B, Seveno R, Tabellout M, Kassiba A 2017 J Appl Phys 122(14) 144101.

[6] Poddar S, Foreman K, Adenwalla S, Ducharme S 2016 Appl Phys Lett 108(1) 012908.

[7] Seveno R, Carbajo J, Dufay T, Guiffard B, Thomas JC 2017 J Phys Appl Phys 50(16) 165502.